Question

A consumer testing agency tested 130 makes and models of cars. In the model below, price (in 1000s) was the dependent variable, and the independent variables included miles per gallon (MPG), Handling score (on a scale from 0 to 5) and Reliability score (on a scale from 0 to 20), as well as a dummy, d_Leather, indicating that the car has a leather interior. The residual plot for MPG is also included.

SUMMARY OUTPUT
Regression Sta tistics
Multiple R													0.719064
R Square													0.517054
Adjusted R Square													0.501599
Standard Error													14.24754
Observations													130
ANOVA
					df					SS						MS					F					Significance F
Regression					4					27166.07						6791.518					33.45699
Residual					125					25374.06						202.9925
Total				129							52540.13
Coefficients			Standard Error						t Stat					P-value				Lower 95%					Upper 95%
Intercept		22.27657						4.912525					4.534647				1.33E-05					12.55407
MPG	1.135804					0.098529						11.52767			2.17E-21				0.940804				31.99907
Handling	0.133298					0.765562						0.174118			0.862054				-1.38184				1.330804
Reliability	0.146641					0.212107						0.691351			0.490627				-0.27315				1.648441
d_Leather	3.784139					2.539686						1.490003			0.138742				-1.24221				0.566427

a. Write the model estimated in the above equation.

b. Is the regression significant overall?

c. What is the interpretation of the coefficient for d_Leather?

d. What is the interpretation of the coefficient for Reliability?

e. Looking at the residual plot, does it look like our assumptions on the error term are sound? What would you recommend to improve the model?

f. Write the new model based on your recommendation from part c.

Answer 1

a. Write the model estimated in the above equation.

The estimated model is,

Price = 22.27657 + 1.135804 MPG + 0.133298 Handling + 0.146641 Reliability + 3.784139 d_Leather

b. Is the regression significant overall?

F test statistic for the Anova test = 33.45699

Numerator df = DF for regression = 4

Denominator df = DF for residual = 125

Critical value of F at 0.05 significance level and df = 4, 125 is 2.44

Since the F statistic (33.45) is greater than the critical value (2.44), we conclude that the regression model is overall significant.

c. What is the interpretation of the coefficient for d_Leather?

Slope coefficient for d_Leather = 3.784139

Keeping all other variables constant, the price difference between car with leather interior and without leather interior is 3.784139 * 1000 = 3784.139

d. What is the interpretation of the coefficient for Reliability?

Slope coefficient for Reliability = 0.146641

Keeping all other variables constant, with unit increase in reliability score, the price of the car increases by 0.146641 * 1000 = 146.641